= Equal-diffusivity magnetorotational channel
{title2=$\omega_A^2=A(2\Omega-A),\quad\gamma=A-\nu k_z^2$}
For $0<A<2\Omega$ and equal <kinematic viscosity> and <magnetic diffusivity>, a vertical wavevector admits $\mathbf v=(V,V,0)$ and $\mathbf b=(i\omega_AV/A,-i\omega_AV/A,0)$ in Alfvén-speed units. Substitution into the <magnetorotational instability> equations gives the displayed frequency and growth rate. In a <Keplerian disk>, growth of this polarization requires $B_z^2/(\mu_0\rho)>5\nu\Omega/4$. This is a bound for this selected channel and its wavelength, not a universal threshold for every MRI mode in an unbounded domain.
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